**Core Concept**
The question is testing the knowledge of the arterial supply to the lower limb and the clinical examination skills required to assess it. The arterial supply to the lower limb is provided by the common iliac arteries, which divide into the external iliac arteries that become the femoral arteries. The femoral arteries then divide into the superficial and deep femoral arteries.

**Why the Correct Answer is Right**
The deep femoral artery is difficult to palpate because it is located deep within the thigh, beneath the sartorius muscle. It is a branch of the femoral artery that supplies blood to the muscles of the thigh. Due to its deep location, it is not easily palpable. The superficial femoral artery, on the other hand, is located more superficially and is easily palpable as the femoral pulse.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not specified, but typically, the superficial femoral artery is not considered difficult to palpate.
**Option B:** This option could be the popliteal artery, but it is actually palpable behind the knee as the popliteal pulse.
**Option C:** This option could be the posterior tibial artery, but it is palpable behind the medial malleolus as the posterior tibial pulse.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that the femoral pulse is a reliable indicator of lower limb perfusion, and its absence can indicate a blockage in the femoral artery.

**Correct Answer: C. Popliteal artery is less commonly used here, but actually the correct answer is the **Popliteal artery** is not the best answer here. The best answer for this option is actually the **Deep femoral artery**.